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Delft University of Technology

Radial polarization and beam shaping to sharpen the electric field in focus

Ushakova, Kate

DOI

10.4233/uuid:7d87bc5b-cf6d-4d73-a870-7da2c4c0d7de

Publication date

2016

Document Version

Final published version

Citation (APA)

Ushakova, K. (2016). Radial polarization and beam shaping to sharpen the electric field in focus.

https://doi.org/10.4233/uuid:7d87bc5b-cf6d-4d73-a870-7da2c4c0d7de

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Radial polarization and beam shaping

to sharpen the electric field in focus

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Stellingen

behorende bij het proefschrift

R A D I A L P O L A R I Z A T I O N AND B E A M S H A P I N G TO S H A R P E N T H E E L E C T R I C F I E L D I N F O C U S

door

Katsiaryna Y. U S H A K O V A

1. Het verlcrijgen van een sterke, smalle longitudinaal elektrische veldcomponent i n het brandpunt door middel van amplitude-, polarisatie- en fasemodulatie van de lichtbundel is een veelbelovende mogelijkheid om de resolutie met 20 -30% te ver-beteren in photolifhografle, laser writing en fluorescentiemicroscopie (zie Hoofd-stulc4).

2. Het gebruik van een polarisatie-gevoelige photoresist in combinatie met de lon-gitudinaal gepolariseerde spot is een mogelijke methode om een tot 60% hogere resolutie te behalen in photolithographie (zie Hoofdstuk 5).

3. Een draadrooster polarisator is een veelbelovend optisch element om een hoge kwaliteit amplitude en polarisatie vorming te verkrijgen over een groot golflengte-bereik (zie Hoofdstuk 3).

4. Fabricatie i n een cleanroom is onderzoek aan de hand van een recept, dat alle ingrediënten bevat maar niet de exacte instellingen en verhoudingen. Het is een kwestie van het juiste recept kiezen.

5. Experimentele opstellingen zijn als een levend organisme: perfect functioneren is mogelijk als elk element zonder fouten werkt.

6. Er is geen goede of slechte ervaring. Er zijn slechts ervaringen waar men wel of geen lessen van leert.

7. Een PhD heeft veel gemeen met een bergtocht. Men heeft de juiste schoenen no-dig en moet meerdere beklimmingen en dalingen volbrengen om om het einde efficiënt te bereiken.

8. Deelname aan meerdere projecten vergroot het succes van elk daarvan.

9. Voorspellen dat de wet van Moore binnenkort zal falen is als voorspellen dat er een eind komt aan de olie en gasreserves: het wordt continu uitgesteld.

10. Traditie en innovatie zijn beiden belangrijk i n het leven. Respect voor de eerste en moed om de tweede te implementeren zorgen voor de balans.

Deze stellingen worden opponeerbaar en verdedigbaar geacht en zijn als zodanig goedgekeurd door de promotor proL dr. H.R Urbach.

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Propositions

accompanying the dissertation

R A D I A L P O L A R I Z A T I O N AND B E A M S H A P I N G TO S H A R P E N T H E E L E C T R I C F I E L D I N F O C U S

by

Katsiaryna Y. U S H A K O V A

1. Obtaining a large, narrowlongitudinal electric field component i n focus via modu-lation of amplitude, polarization and phase of the light beam is a potential tool for up to 20 - 30% resolution enhancement i n photolithography, direct laser writing and fluorescence microscopy (see Chapter 4).

2. Utilization of polarization-selective photoresist with longitudinally polarized spot can become candidate for up to 60% resolution enhancement i n photolithography (see Chapter 5).

3. Wire grid polarizer is a promising optical element to perform high quality light beam amplitude and polarization shaping i n a broadband wavelength range (see Chapters).

4. Fabrication i n a clean room is research according to a raw recipe: all ingredients but no precise settings and ratios are known. It is a matter of flnding a good initial recipe.

5. Experimental set-up is like a living organism: its perfect working is possible pro-vided every element is functioning without failure.

6. There is no good or bad experience. There is experience one gets or does not get the lesson from.

7. PhD has something in common with a hiking route. One needs appropriate shoes to reach quickly and effectively its end while malcing multiple uphills and down-hills on the way.

8. Participation in multiple projects triggers success in each of them.

9. Predicting a quick failure of Moore's law is like predicting the end of petrol and gas reserves; it is being continuously postponed.

10. Tradition and innovation are botir important in one's Ufe. Itespect for the flrst and courage to implement the later make its balance.

These propositions are regarded as opposable and defendable, and have been approved as such by the promotor prof. dr. H.E Urbach.

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R A D I A L P O L A R I Z A T I O N A N D B E A M S H A P I N G

T O S H A R P E N T H E E L E C T R I C F I E L D I N F O C U S

P r o e f s c h r i f t

ter v e r k r i j g i n g v a n de graad van doctor aan de Technisclie Universiteit Delft,

op gezag van de Rector M a g n i f i c u s prof. ir. K.C.A.M. L u y b e n , voorzitter v a n het College voor Promoties,

i n het openbaar te verdedigen op 12 October 2016 o m 10:00 u u r

door

K a t s i a r y n a U S H A K O V A

Master of Science i n Physics a n d Mathematics, Belarusian State University, M i n s k , Belarus,

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D i t p r o e f s c h r i f t is goedgelceurd door de p r o m o t o r : c o p r o m o t o r : P r o f d r H.R U r b a c h Dr. S.F. Pereira Samenstelling p r o m o t i e c o m m i s s i e : Rector M a g n i f i c u s , Prof. d r H.E U r b a c h , Dr. S.F. Pereira, voorzitter Technische Universiteit D e l f t Technische Universiteit D e l f t Onafliankelijke leden: Prof. d r i r G.V V d o v i n , Prof. d r i r D.1. Broer, Prof. d r i r V Zwiller, Ing. I . M . W i j n , Dr. i n g . A.J. den Boef, Prof. dr. i r N . de l o n g . Technische Universiteit D e l f t Technische Universiteit E i n d h o v e n K T H (Sweden) V D L ETG T & D A S M L

Technische Universiteit D e l f t , reservelid

This research was f i n a n c i a l l y s u p p o r t e d by the Stichting voor Technische Wetenschap-p e n STW (Wetenschap-project 10727)

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V

Keywords: a m p l i t u d e , phase, p o l a r i z a t i o n m o d u l a t i o n , atomic force microscopy, anisotropic m e d i u m , d i f f r a c t i v e optics, direct laser w r i t i n g , f i n i t e element m e t h o d , focused radially polarized light, Lagrange m u l t i -plyer rule, lithography, m e t a l l i c grating, near U V light, l i q u i d crystal, anisotropic p o l a r i z a t i o n selective resist, physical optics, r e s o l u t i o n enhancement, RichardsWolf d i f f r a c t i o n integral, scanning electron m i -croscopy, spatial l i g h t m o d u l a t o r , w i r e grid p o l a r i z e r

Printed by: I p s k a m p Drukkers B V

Front & Back: Pixelated image of the p i c t u r e "Over the t o w n " by Marc Shagall. A pixel size is 60% smaller i n the f r o n t cover t h a n i n the back cover.

Copyright © by K. Ushakova ISBN 978-94-028-0364-8

A n electronic version of this dissertation is available at h t t p : / / r e p o s i t o r y . t u d e l f t . n l /.

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C O N T E N T S

S u m m a r y 11

Samenvatting 13

Abbreviations 15

1 Introduction 17

1.1 Lithography applications I'or a resolution i n i | ) r o \ ' c i i u ' n l using a l i g h l l y f o

-cused l o n g i l t i d i n a l electric field c o m p o n e n t 17

1.2 The foctissing o f light: ft o m tlie scalar to the vectorial approach 21

1.2.1 linage l o n n a l i o i i i n air 21

1.2.2 P r i n t i n g focused spots in a photoresist: Dill's m o d e l , photoisesist

l e s p o i i s e 24 1.3 I'loject " I l i g l i l e s o l u l i o i i l i l l i ( 4 ; i a p h y u s i i i ; . ; u i R - o i n i M i t i o i i a i p o l a i i / a l i o n states o f light" 26 1.4 I l i e M l L i c U i i ( M ) f the Ihesis 27 References 28 Appendix A 31 References 35

2 Experimental Set-up, IMethods and Instrumentation 37

2.1 Geneial description 37

2.2 Laser source 38

2.3 .Ainplitude i n o t k i l a l i o n 39

2.4 Ucalization o t i a d i a l l y polarized lighl w i t h a Ilal phase c l i s l r i h i i l i n n l o r i n a

-t i o n 40

2.5 Photoresists p i e i i n i a t i o n and (levelopmenl procecliiies 41

2.5.1 C o m m e r c i a l photoresist sam|)les 4 1

2.5.2 Polarization-sensitive photoresist sani|iles 42

2.6 f i x p e r i m e n t a l procedure 45

2.6.1 M a i n experimental parameters. F i n d i n g o f the o p t i m a l focus 45

2.6.2 l.ahVipvv program 46

References 47

Appendbc B 49

3 Wire Grid Polai izer 51

3.1 I n t r o d u c t i o n 51

3.2 Design of the WGP based on IT.M s i m u l a t i o n s 52

3.3 Experiment: f a b r i c a t i o n process 58

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C O N T E N T S

3.4 l - x p i M i i n c M i l a l xxM i f i r a l i o i u i f l h o |KMT(n i n a i H (M)rilK'l'nbricatc'cl VV(;i'. . . . . 60

3.4.1 Spectral visil)ilily of the VVGP using a w h i t e light polarization m i

-croscope 60

3.4.2 Absolute transmission, transmiltcci ratio TMITE o f the WGP by

means of p i n l i o l e scanning technicjtie at 405 n m and c o m p a r i s o n

w i t h ihcoreiical results 61

3.4.3 i l o n i o j i c i i c i l y ol raclially polaiized liglit 63

3.4.4 M c a s u i f i n c i i l of the t|ualily of tlie focused spot 63

3.4.5 h i i p l e i i i e n l a l i d n of tlie v a r y i n g geoiiied y VVGP 65

3.5 Conclusions 68

References 68

Appendix C 73

3.5.1 Some details about f a b r i c a t i o n steps of tiie f i n a l recipe 73

3.5.2 V a r y i n g g e o m e t r y WGP f a b r i c a t i o n details 73

4 C o m m e r c i a l Resist 77

4.1 I n t r o d n c l i o n 77

4.2 Theory 78

4.3 I xperiiiieiit 81

4.3.1 Resist samples preparation, exposures and development 81

4.3.2 .Set-up 82

4.3.3 Inspection of the samples 84

4.4 Results and discussion 85

4.5 c o n c l u s i o n s 89

References 89

Appendix D 93

References 95

5 Polarization-selective Resist 97

5.1 I n t r o d u c t i o n 97

5.2 Experimental 98

5.2.1 Focused ladially polarized laser set-up 98

5.2.2 Photoresist 99

5.3 Results and discnssion 100

5.3.1 Deeoinposition of radially and linearly polarized lighl into l o n g i l i i

dinal and tiansv iMse c o n i p o n e i i t s inside the photoresist 100

5.3.2 I low doesanisotropy of polarization-selective pliotoresist influence

on focused spot 102

5.3.3 Polarization-selectivitA'of the photoresist 102

5.3.4 Resolution 103

5.4 Conclusions 105

Ueferences 106

Appendix E 109

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C O N T E N T S

6 Conclusions

Acknowledgements

C u r r i c u l u m Vitae

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S U M M A R Y

The progress i n l i t h o g r a p h y takes its i m p u l s e f r o m Moore's law. It states that the n u m b e r of transistors i n integrated circuits doubles every 1.5 year a n d that the costs of transistors w i l l d i m i n i s h by consequence. The need f o r smaller sized transistors stimulates the de-v e l o p i n e n t of next-generation l i t h o g r a p h y technologies and pushes o p t i c a l l i t h o g r a p h y to its l i m i t s . The m o t i v a t i o n f o r this PhD thesis research originates f r o m recent theoret-ical results s h o w i n g that o p t i m a l l y a m p l i t u d e - s h a p e d radiaUy p o l a r i z e d light produces a very tight l o n g i t u d i n a l electric f i e l d c o m p o n e n t i n focus. I f this l o n g i t u d i n a l electric f i e l d can be isolated f r o m the other c o m p o n e n t s by, f o r example, selectively p r i n t i n g i n a photoresist, t h e n a n increase of resolution can be achieved.

E x p e r i m e n t a l i m p l e m e n t a t i o n of this research w o u l d n o t be possible w i t h o u t an app r o app r i a t e theoretical b a c k g r o u n d . Vector d i f f r a c t i o n theory, valid f o r general o app t i c a l f o -cusing systems w i t h h i g h n u m e r i c a l aperture i n w h i c h l i g h t p o l a r i z a t i o n s h o u l d be taken i n t o account, is the proper theory that has to replace classical scalar d i f f r a c t i o n theory. An i n s p i r a t i o n f o r our experiments comes f r o m works o f S. Quabis et al., a n d later H . E U r b a c h et al. Here, the authors consider the role of the state of p o l a r i z a t i o n , the a m p l i -tude a n d the phase o f the light i n v i e w of d g h t i n g o f d i e electromagnetic f i e l d i n focus by u t i l i z a t i o n o f the Richards-Wolf integral vector d i f f r a c d o n theory. I n Urbach's w o r k , the s o l u t i o n of Üie o p t i m i z a d o n p r o b l e m predicts a field i n the entrance p u p i l o f the lens, such that the l o n g i t u d i n a l electric c o m p o n e n t at the f o c a l p o i n t is m a x i m u m f o r the given power flow. The q u e s t i o n t h e n arose h o w to realize this o p t i m u m p u p i l field experimentally.

I n this thesis, an e x p e r i m e n t a l p r o o f is given w h i c h shows that the o p t i m u m radially polarized p u p i l field gives a tightly focused l o n g i t u d i n a l electric field c o m p o n e n t i n the focal region. The e x p e r i m e n t a l realization includes research o n design, f a b r i c a t i o n and i m p l e m e n t a t i o n of a circular w i r e grid polarizer (WGP) to shape h i g h - q u a l i t y radially polarized l i g h t i n the near U V wavelength range. Other research topics are the m a n u -f a c t u r i n g o-f the e x p e r i m e n t a l -focussing set-up w h i c h includes the WGR o -f a spatial light m o d u l a t o r (SLM) to m o d u l a t e the a m p l i t u d e a n d of a spiral phase plate (SPP) to realize the o p t i m u m constant phase t h r o u g h o u t the p u p i l . A LabView p r o g r a m , s y n c h r o n i z i n g the laser, the pulse generator a n d the movements of the XYZ piezo stage, manages the experiment. A h i g h - N A objective lens focuses the laser l i g h t o n a photoresist sample, m o u n t e d o n the XYZ piezo stage to enable recording of t h r o u g h - f o c u s arrays. The goal of the e x p e r i m e n t is to realize the ideal a m p l i t u d e and phase m o d u l a t e d radially polar-ized light field d i s t r i b u t i o n i n the entrance p u p i l of the h i g h - N A objective to get the large l o n g i t u d i n a l electric field c o m p o n e n t i n the photoresist w h i c h is substantially narrower t h a n a classical A i r y spot. The o p t i m u m electric field d i s t r i b u t i o n is radially polarized light w i d i its a m p l i t u d e increasing i n a specific way towards the r i m of the p u p i l a n d the

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x i i S U M M A R Y

electric field vectors being i n phase across the entire p u p i l . The detailed d e s c r i p t i o n of the o p t i c a l a n d electronic c o m p o n e n t s and of the c o m m e r c i a l resist p r e p a r a t i o n proce-dure are provided, as w e l l as the m a i n experiment flow chart a n d data analysis based o n a t o m i c force a n d scanning electron m i c r o s c o p y methods.

W h e n focused i n the resist, the radially polarized l i g h t has also a transverse elec-tric field c o m p o n e n t , w h i c h can be significantiy w i d e r t h a n that of a c o n v e n t i o n a l A i r y pattern. Therefore, to m a i n t a i n the r e s o l u t i o n h i g h , the l o n g i t u d i n a l c o m p o n e n t of the electric field i n focus s h o u l d be selectively p r i n t e d . This has been achieved here by either m o d i f y i n g the a m p l i t u d e d i s t r i b u t i o n of the field i n the p u p i l a n d / o r by u s i n g a resist, that is o n l y sensitive to the l o n g i t u d i n a l electric field c o m p o n e n t . A p r o o f - o f - c o n c e p t resolution e n h a n c e m e n t based o n a n e w l y developed polarizationselective resist is i m -p l e m e n t e d . A m u l t i d i s c i -p l i n a r y a-p-proach via i n t e g r a t i o n of l i q u i d crystal c h e m i s t r y i n the development o f an advanced o p t i c a l a p p l i c a t i o n has been f o l l o w e d . This has been p e r f o r m e d i n c o l l a b o r a t i o n w i t h the F u n c t i o n a l Organic Materials & Devices G r o u p o f the Technical I f n i v e r s i t y of Eindhoven. The final recipe of the polarization-selective re-sist is p r o v i d e d . We show experimentally that flie F W H M of the radially p o l a r i z e d l i g h t spot focused i n this specially developed p o l a r i z a t i o n sensitive resist, can be u p to 56% smaller c o m p a r e d to an isotropic resist. The results have been c o n f i r m e d by s i m u l a t i o n s c o n d u c t e d w i t h a rigorous electromagnetic solver based o n RichardsWolf vector d i f f r a c -t i o n in-tegral.

To summarize, techniques to t i g h t e n the focused spot, by a m p l i t u d e , phase a n d p o -larization shaping of the field i n the p u p i l a n d by the u t i l i z a t i o n of a n e w l y synthesized polarization-selective photoresist, are demonstrated. The e x p e r i m e n t a l m e t h o d s devel-oped i n this thesis, based o n theoretical models of the tight f o c u s i n g p r o b l e m , pave the way f o r a study of advanced o p t i c a l applications.

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S A M E N V A T T I N G

De v o o r u i t g a n g i n littiografie w o r d t gedreven door de Wet van Moore, die voorspelt dat het aantal transistors op een g e ï n t e g r e e r d circuit elke 1,5 jaar verdubbelt. Als gevolg daarvan dalen de p r o d u c t i e k o s t e n van transistoren. De behoefte aan kleinere transistoren s t i m u l e e r t zowel de o n t w i k k e l i n g v a n de volgende generatie lithografie t e c h n o l o -gie als ook het verleggen van de grenzen van optische lithografie. De d r i j f v e e r achter d i t PhD onderzoek ligt i n recent theoretisch w e r k w a a r i n w o r d t aangetoond dat o p t i m a a l a m p l i t u d e gemoduleerd, radieel gepolariseerd ficht i n het b r a n d p u n t een sterk gecon-centreerd l o n g i t u d i n a a l veld heeft als het gefocusseerd w o r d t . Als deze v e l d c o m p o n e n t g e ï s o l e e r d k a n w o r d e n van de andere v e l d c o m p o n e n t e n door deze selectief te p r i n t e n m e t een resist of m e t fiuorescentie, k a n een verhoogde resolutie w o r d e n bereikt.

Experimentele u i t v o e r i n g v a n d i t werk zou n i e t m o g e l i j k z i j n zonder de o n t w i k k e l i n g van een geschikte theoretische achtergrond. V e c t o r i ë l e diffractietheorie, algemeen gel-d i g v o o r focusserengel-de optische system m e t een hoge n u m e r i e k e apertuur voor gevallen w a a r i n m e n rekening dient te h o u d e n m e t polarisatie is hier een vereiste. D i t i n vergelij-k i n g t o t vergelij-klassievergelij-ke theorie die veelal gebaseerd is op scalaire diffractietheorie. Inspiratie voor onze e x p e r i m e n t e n k o m t u i t het w e r k v a n S. Quabis et a l , en later H.R U r b a c h et al. Deze auteurs b e s c h r i j v e n de r o l v a n polarisatie effecten, a m p l i t u d e en fase van l i c h t o p het elektromagnetische veld i n focus m e t b e h u l p v a n de Richards-Wolf integraal. Het o p t i m a l i s a t i e p r o b l e e m o m de ideale elektrische v e l d d i s t r i b u t i e i n de i n g a n g s p u p i l van de lens te v i n d e n waarmee het l o n g i t u d i n a l e elektrische veld i n focus gemaximaliseerd w o r d t , v o o r een gegeven vermogensflux, is opgelost. D i t nodigde u i t tot experimentele verificatie.

I n deze scriptie w o r d t het experimentele bewijs geleverd dat het optimale, radieel gepolariseerde p u p i l v e l d een sterk gefocusseerde l o n g i t u d i n a l e elektrische v e l d c o m p o n e n t oplevert i n het brandvlak. De experimentele u i t v o e r i n g o m v a t het o n t w e r p , de f a -bricage en i m p l e m e n t a t i e van een cirkelvonnige draadrooster polarisator (WGP) o m een hoge kwaliteit van radieel gepolariseerd l i c h t te v e r k r i j g e n n a b i j het U V handbereik. Een ander deel v a n het onderzoek o m v a t het o n t w e r p e n en samenstellen v a n de optische opstelling, inclusief WGP, spatial l i g h t m o d u l a t o r (SLM), en spiraalvormige fase plaat (SPP) v o o r het m o d u l e r e n v a n a m p l i t u d e en de fase v a n het p u p i l v e l d . Een LabView p r o g r a m m a dat de laserpulsen synchroniseert m e t de verplaatsing v a n een XYZ piezo element bestuurt het experiment. Op het piezo element is een h o o g N A objectief g e m o n -teerd dat het l i c h t op een fotoresist focusseert, zodat i n e n controle heeft over de positie van de fotoresist ten opzichte van het brandvlak. Het doel v a n het e x p e r i m e n t is o m de o p t i m a l e a m p l i t u d e en fase m o d u l a t i e te realiseren van de radieel gepolariseerde v e l d d i s t r i b u t i e i n de i n g a n g s p u p i l van het h o o g N A objectief o m daarmee een sterke l o n g i t u -dinale elektrische v e l d c o m p o n e n t te v e r k r i j g e n i n de fotoresist die substantieel smaller is dan de klassieke A i r y schijf. De o p t i m a l e elektrische v e l d d i s t r i b u t i e is radieel gepolari-seerd m e t een a m p l i t u d e die toeneemt i n de r i c h t i n g v a n de rand v a n de p u p i l , t e r w i j l het

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x i v S A M K N V M T I N C ;

elektrisclie veld over de gehele p u p i l i n fase b l i j f t . De gedetailleerde b e s c h r i j v i n g van op-tische en elektronische c o m p o n e n t e n , de c o m m e r c i ë l e resist verwerkingsprocessen, het h o o f d e x p e r i m e n t e n data analyse gebaseerd o p a t o m i c force en s c a n n i n g electron m i -croscope t e c h n i e k e n w o r d e n verstrekt, evenals de experimentele procedure en de data analyse die gebaseerd is op a t o m i c force en scanning electron microscopie m e t h o d e n .

Bij focusseren i n de resist h e e f t het radieel gepolariseerd l i c h t ook een transversale elektrische v e l d c o m p o n e n t , die significant breder k a n z i j n dan de gebruikelijke A i r y schijf. O m desondanks een hoge resolutie te behouden, is n o d i g dat m e n de l o n g i t u d i n a l e v e l d -c o m p o n e n t sele-ctief k a n p r i n t e n . D i t is hier bereikt door de a m p l i t u d e d i s t r i b u t i e v a n het p u p i l v e l d aan te passen e n / o f het gebruik v a n een resist die slechts gevoelig is v o o r de l o n g i t u d i n a l e elektrische v e l d c o m p o n e n t . Een p r o o f - o f - c o n c e p t resolutievergroting ge-baseerd op de recent o n t w i k k e l d e polarisade-gevoelige resist is h i e r g e ï m p l e m e n t e e r d . D i t k w a m t o t stand door een m u l t i d i s c i p l i n a i r e aanpak w a a r i n LC (vloeibare kristal) che-m i e is g e ï n t e g r e e r d i n de o n t w i k k e l i n g v a n een geavanceerde optische toepassing. D i t is u i t g e v o e r d i n s a m e n w e r k i n g m e t de F u n c t i o n a l Organic Materials & Devices Group v a n de T U Eindhoven. Details van het recept van de polarisatie-gevoelige resist w o r d e n verstrekt. We demonstreren d o o r m i d d e l v a n e x p e r i m e n t e n dat de F W H M v a n het gefo-cusseerde radieel gepolariseerde l i c h t i n deze speciaal o n t w i k k e l d e polarisatie-gevoeUge resist tot 56% kleiner k a n z i j n i n v e r g e l i j k i n g t o t een isotrope resist. De resultaten w o r d e n bevestigd door simulaties uitgevoerd m e t een rigoureuze elektromagnetische veldoplos-ser gebaseerd op de Richards-Wolf v e c t o r i ë l e diffractie-integraal.

Samengevat, twee technieken o m het b r a n d p u n t te verkleinen w o r d e n g e d e m o n -streerd, door m i d d e l v a n a m p l i t u d e , fase en polarisatie m o d u l a d e v a n het p u p i l v e l d en door het gebruik v a n een recent gefabriceerde polarisade-gevoelige fotoresist. Ex-p e r i m e n t e l e m e t h o d e n o n t w i k k e l d i n d i t onderzoek, gebaseerd oEx-p de theoretische be-s c h r i j v i n g v a n be-sterk focube-sbe-seren, leggen de grondbe-steen v o o r verder onderzoek aan gea-vanceerde optische toepassingen.

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A B B R E V I A T I O N S

A F M a t o m i c force microscopy Ag silver Al a l u m i n u m Au g o l d BS b e a m splitter BSS b e a m step size CCD c o u p l e d charge device DR d i l u d o n rate

EBPC electron b e a m p a t t e r n generator

FEM finite element m e t h o d

FFT fast Fourier t r a n s f o r m

F W H M f u l l Mfidth at half m a x i m u m

CLP Glan Laser polarizer

H W H M h a l f w i d t h at h a l f m a x i m u m

IPA isopropyl alcohol

IR i n f r a r e d

Ir i r i d i u m

LC l i q u i d crystal

LCoS l i q u i d crystal o n silicon

M I B K m e t h y l i s o b u t y l ketone

NA n u m e r i c a l aperture

PGMEA propylene glycol m o n o m e t h y l ether acetate

PSF p o i n t spread f u n c t i o n

RCA standard cleaning steps developed i n RCA (Radio C o r p o r a f i o n of America)

r p m revolutions per m i n u t e

SEM scanning electron microscopy

SLM spatial Hght m o d u l a t o r

SPP spiral phase plate

STW Stichting voor Technische Wetenschappen

TE transverse electric

T M transverse magnetic

UV-VIS ultraviolet visible

VLL Van Leeuwenhoek Laboratory

WGP w i r e grid polarizer

I D one d i m e n s i o n a l

2D two d i m e n s i o n a l

3D three d i m e n s i o n a l

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Jl

I N T R O D U C T I O N

1 . 1 . L I T H O G R A P H Y A P P L I C A T I O N S F O R A R E S O L U T I O N I M P R O V E

M E N T U S I N G A T I G H T L Y F O C U S E D L O N G I T U D I N A L E L E C -T R I C F I E L D C O M P O N E N -T .

The 2015 "Market & Technology" report e n t i t l e d "Photolithography E q u i p m e n t and M a -terials f o r Advanced Packaging, M E M S a n d LED A p p l i c a t i o n s " describes the current state-o f - t h e - a r t i n the s e m i c state-o n d u c t state-o r industry, d r i v e n by trends i n c l u d i n g technstate-olstate-ogy dstate-ow?n- dow?n-scaling, cost r e d u c t i o n and increasing f u n c t i o n a l i t y [ i ] . This r e p o r t advocates f u r t h e r research i n order to p u s h p h o t o l i t h o g r a p h y to its l i m i t s , either by m a i n t a i n i n g Moore's

law or by a d d i n g f u n c t i o n a l i t y . Fig. ! i shows the progress over the last decade towards

m i n i a t u r i z a t i o n t h r o u g h c o m p a r i s o n of sizes of s e m i c o n d u c t o r m a n u f a c t u r i n g process nodes w i t h some m i c r o s c o p i c objects a n d visible l i g h t wavelengths. A c c o r d i n g to I n -tel [2], the pace o f advancement of Moore's l a w has slowed, starting at the 22 n m n o d e a r o u n d 2012, and c o n t i n u i n g at 14 n m i n 2015. This is scheduled to h o l d t h r o u g h the 10 n m n o d e i n late 2017.

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2 1. I N T R O D U C T I O N 10^In t^tlJOOimmvelengthj

w

\ \ \ \ \

/

180 m i (1999) e.g. Coppemiim E m m (2000) e.g. Powerf"C7447 _ 9O_nm(2002)c.g,VIACT ,65 nm (2006) e.g. Core Duo

,45nni(20Ce) e.g. Core 2(Wolfda'e) ,32 rm (2010) e.g Core i3 (Claikd 22 nm (2011) e.g. Xeon E3-1230

16 m i (C2013) U n n i ( c 2 0 1 5 )

5t3phyhm

auras bxtet 5txmiat:osx>n head

/mil

fiBdUcodcel ooss^ecbon

HmianinrDmo d^iency virus iHIV)

Figure 1.1: Sizes of semiconductor manufacturing process nodes inthe period of 1970-2015 ( ].

A s i m p l i f i e d w o r l d n g p r i n c i p l e o f die mask p h o t o l i t h o g r a p h y technique is as foUows. A light beam, e m i t t e d f r o m a source, c o l l i m a t e d by a series o f condenser lenses, i l l u -minates a mask. T h e mask contains patterns that are i m a g e d by a l i t h o g r a p h i c lens o n t o a substrate w i t h a layer o f a photoresist. T h e photoresist consists o f photosensi-tive molecules w h i c h undergo a c h e m i c a l reaction i n d u c e d by light. This change allows the user to remove either the exposed or unexposed p a r t d e p e n d i n g o n the type o f the photoresist. T h e exposed areas become soluble w h i l e the unexposed areas r e m a i n insol-uble i n the case o f positive photoresists; the opposite occurs f o r negative photoresists. Fig. I ' illustrates these processes after the exposure.

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1.1. LiTHOCiRAPlIYAI'l'l.lCATTONS POR A RP.SOl.UTION 1M 1'ROVEMF.Nl IJSINC, A r i C H T I . Y

F O C U S E D L O N G I T U D I N A I . E L E C T R I C FIIILD C O M I ' O N L N L. 3

Figure 1.2: Positive and negative tone photoresists upon exposure in the photolithograpliy process.

A l t h o u g h mask p h o t o l i t h o g r a p h y is the m o s t widely used technology f o r c h i p f a b r i -cation, other techniques can be advantageous f o r small scale p r o d u c t i o n or c o m p l e x 3 D structures. A m o n g t h e m , direct laser w r i t i n g technology, also k n o w n as maskless l i t h o g -raphy, is capable of m a n u f a c t u r i n g 3 D objects w i t h h i g h f i d e l i t y a n d r e s o l u t i o n 1 i ] .

heioelectrk 3D c a n n i n g Stage

Inverted Micfoicope

Beam Expsniion

Figure 1,3: Set-up for direct laser writing [ ]

Instead o f a mask, an electronicafly designed file is used to draw patterns o n t o a p h o -toresist. M u l t i p l e Gaussian beams f r o m a raster scan laser w r i t e r create microstructures

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4 1. IN I K O U U C T I O N

Femtosecond pulse

Figure 1.4: Two-photon absorption process.

(Fig 1 ..3). Tiie beams' intensities ai-e m o d u l a t e d by an acousto-optic m o d u l a t o r (AOM) or a spadal l i g h t m o d u l a t o r (SLM) according to a design file. I n the case o f SLM, a c o n v e n -t i o n a l re-ticle is replaced by a " p r o g r a m m a b l e p a -t -t e r n mask", w h i c h is a n array o f pixels. T h e n , directed by a n acousto-optic deflector (AOD), l i g h t is focused by a lens o n t o the m o v i n g substrate. A photoresist layer o n the substrate is exposed one stripe at a t i m e by successive scans. A p p l i c a t i o n o f the p a t t e r n to the entire substrate f r o m the stripes is accomplished by s t e p p i n g the sample i n the d i r e c t i o n perpendicular to scanning. I n m u l t i p h o t o n lithography, a t i g h t l y focused f e m t o s e c o n d laser b e a m induces m u l t i -p h o t o n a b s o r -p t i o n i n the -photoresist (Fig. I . ! ) . Very l i t d e ex-posure o f the -photoresist occurs away f r o m the central focal area, since the type o f the photoresist used is n o t sensitive to a single p h o t o n . T w o - p h o t o n a b s o r p t i o n m a i n l y takes place very near the g e o m e t i i c a l focus. As usual, the resolution o f die resulting structure is l i m i t e d by a size of the focal spot. B u t tiie effective size o f the f o c a l spot is reduced by \/2 due to the square-law exposure behaviour o f die photoresist. 3D patterns can be f a b r i c a t e d w i t h 3 D scanning o f the laser beam.

Direct laser w r i t i n g technologies can b e n e f i t f r o m lateral resolution enhancement. Therefore, the experimentally realized p r o o f o f the p r i n c i p l e of isolation o f a tightly f o -cused l o n g i t u d i n a l electric field c o m p o n e n t , to w h i c h this thesis is dedicated, is applica-ble to direct laser w r i t i n g technologies.

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1.2. T i l l' : i-ociJSSiNC o i ' I.I C I I T: I R O.M T H E S C A L A R T O T I I L: \ T C I O H I A I A P I M U I X C I I 5

1 . 2 . T H E F O C U S S I N G O F L I G H T : F R O M T H E S C A L A R T O T H E V E C -T O R I A L A P P R O A C H

1.2.1.

I M A G E F O R M A T I O N I N A I R

: 'H E classical theory of scalar d i f f r a c t i o n n o r m a l l y describes the field i n the f o c a l plane of a lens under the paraxial a p p r o x i m a t i o n t()-H]. Given a certain field d i s t r i b u t i o n at the f r o n t f o c a l plane of a lens, the resulting field at the back focal plane is p r o p o r f i o n a l to the Fourier t r a n s f o r m of the c o m p l e x a m p l i t u d e of the field i n the f r o n t focal plane scaled by the p r o d u c t of the wavelength and the focal l e n g t h . I n the s i m p l e case of focussing a field of u n i f o r m a m p l i t u d e a n d constant phase (plane wave), one obtains the w e l l k n o w n A i r y p a t t e r n whose intensity is given by:

where k is the peak intensity, rz is the distance f r o m the center of the spot at the focus plane, A is the wavelength, D is the lens diameter a n d ƒ is the focal length. The radius of the spot, d e f i n e d as the distance f r o m the center to the first zero m i n i m u m of the A i r y disk, is rs = l.llAflD.

The scalar approach however is n o t v a l i d f o r a l l o p t i c a l systems. One of the f u n d a m e n -tal p r o p e r f i e s of the l i g h t as electromagnetic wave is that i t is a transverse wave as f o u n d f r o m the s o l u t i o n of JVIaxwell's equations. Polarization of the light is a direct consequence of this property, b u t f o r low n u m e r i c a l aperture o p t i c a l systems the p o l a r i z a t i o n o f a b e a m between the source and focus is essentially u n c h a n g e d a n d thus m a y be i g n o r e d by u s i n g scalar d i f f r a c t i o n theory f o r l o w n u m e r i c a l aperture lens optical systems. I n our case, a h i g h n u m e r i c a l aperture (NA) focussing system is employed. Therefore, the ef-fect of the p o l a r i z a t i o n properties of the fight beam u p o n focussing becomes i m p o r t a n t . A m o r e general t h e o r y is needed to describe d i e field at focus: vector d i f f r a c f i o n the-ory. O r i g i n a t i n g f r o m Ignatowsky d i f f r a c t i o n t h e o r y [9], as later elaborated i n [i l l, i I],the s o l u f i o n is c o m m o n l y refered to as vector Richards-Wolf d i f f r a c t i o n integral.

The converging spherical wave is expanded i n terms of plane waves i n d i f f e r e n t d i -rections (the so-called angular s p e c t r u m ) . The evolving field is calculated by c o m b i n i n g the c o n t r i b u t i o n s f r o m each plane wave c o m p o n e n t after p r o p a g a t i n g to the p o i n t i n question. T h e n , assuming a lens free of aberrafions, the electric field i n focus can be w r i t t e n as

(1.1)

A(A:.v, A;,,) exp (;'k • (r2 - r i ) ) d f c v d A ; , , (1.2)

r i a n d tz correspond to the focal p o i n t and the p o i n t of observation w i t h the coordinate system o r i g i n at the center of the lens a n d the z d i r e c f i o n along the lens' axis. D refers to the solid angle made by the lens as seen f r o m the focus w h i c h fimits the range of k

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6 1. l l i O D I I C I I O . N

according to fc,. + kj, < k'^NA^. fc.v, ky a n d kz are c o m p o n e n t s of the k , so fc^. + ky + kl = | k | ^ . A(fc.v, ky) is the electric field describing each plane wave c o m p o n e n t .

Further details of the c a l c u l a t i o n of the focused field c o r r e s p o n d i n g to die case of linear a n d o f radial p o l a r i z a f i o n are given i n .Appcntli.x A. By n u m e r i c a l i n t e g r a f i o n [12], based o n the vector RichardsWolf d i f f r a c t i o n integral, we calculate the x, y, z c o m p o -nents of the electric field a n d the net m a g n i t u d e of the electric field a r o u n d the focus. It is i m p o r t a n t to note, that i n the case of f o c u s i n g by a h i g h N A lens, w i t h p o l a r i z a t i o n taken i n t o account, the focussed field has a p o l a r i z a t i o n w h i c h varies across the f o c a l spot. This is clearly illustrated i n Fig. I where the l i n e a r l y p o l a r i z e d l i g h t (along the x d i r e c t i o n at the i n p u t o f the lens) produces n o t o n l y a field i n focus that is linearly p o -larized i n the same d i r e c t i o n b u t also i n the other two o r t h o g o n a l c o m p o n e n t s (y- a n d Z-).

0

Figure 1.5: Intensities of the x - (a), y - (b), z - (c) components and total intensity - (d) at focus in air due to incident linearly polarized light along the x direction at the NA=0.9 lens pupil, x and y axes are labelled in units of A. For each plot the image scale (right of the plot) is set according to that plot's peak value. The plots are normalized to tlie peak (on axis) intensity jfoP = \Eioi{0,0)\^.

A second c o n c l u s i o n is that, a l t h o u g h the lens is cylindrically s y m m e t r i c about fiie z axis, p o l a r i z a t i o n of the i n c i d e n t field i n one d i r e c t i o n results i n a field at the focal plane w h i c h is n o t cyUindrically s y m m e t r i c (see Fig. I.,'), total field i n t e n s i t y ) .

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1.2. TTlK F O C U S S I N G O F L I G H T : FROM T H F SCALAR TO T H F VFCTORIAI. APPROACH 7

radial p o l a r i z a t i o n , as s h o w n i n Fig. i ! . a radially p o l a r i z e d laser b e a m results i n i

i n t e n s i t y a n d includes a large l o n g i t u d i n a l i n a n a r r o w region a r o u n d the focus.

F r o m this f i g u r e one can see that focussing I cyUindrically s y m m e t r i c b e a m f o r the t o t a l c o m p o n e n t ( p o l a r i z a t i o n i n the z d i r e c t i o n ) x,CX) b) 0.8 0.6

Figure 1.6: Intensities of the x - (a), y - (b), z - (c) components and total intensity - (d) at focus in air due to incident radially polarized hght at the NA=0.9 lens pupil, x and y axes are labelled in units of A. For each plot the image scale (right of the plot) is set according to that plot's peak value. The plots are normalized to the peak (on axis) intensity |£ol^ = |£'rof(0,0)|2.

By analysing the profiles o f the d i f f e r e n t f i e l d components, as s h o w n i n Fig. i , one can observe that c o n s i d e r i n g the t o t a l intensity (|Ep) at focus the h a l f w i d t h at h a l f max-i m u m o f d max-i e spot smax-ize w max-i t h l max-i n e a r l y x-polarmax-ized max-i l l u m max-i n a t max-i o n ( H W H M j j , " = 0.375 A along the X axis a n d HWHM['^1 = 0.281 A along the y axis) is smaller t h a n w h e n the i l l u m i n a t i o n is radially p o l a r i z e d {HWHM'f"f ~ 0.389 A) . However, o n l y c o n s i d e r i n g the l o n g i t u d i n a l (z) p o l a r i z a t i o n c o m p o n e n t at focus, the H W H M o f the spot i n the case o f radial p o -l a r i z a t i o n ( H W H M J " ^ =; 0.255 A) is sma-l-ler t h a n that u s i n g -linear p o -l a r i z a t i o n even as measured along the narrower (y) d i r e c t i o n ( H W H M ' / , . " , , ^ , , = 0.281 A). T h e p r o f i l e s f o r the X , y a n d z c o m p o n e n t s {Ex, Ey, a n d Ez) o f focussed l i n e a r l y polarized light (along the x a n d y directions) and radially p o l a r i z e d light are s h o w n i n Fig. i . 7 a, b a n d c, respectively.

Thus, the p o l a r i z a t i o n state o f the light influences the size o f the focused spot i n the case o f h i g h NA. Sensitivity to o n l y the l o n g i t u d i n a l c o m p o n e n t at focus p r o d u c e d u s i n g

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8 1. i N T I i O D U C I I O N

Figure 1.7: Profiles ofthe intensities ofthe longitudinal and transverse components and total intensity at focus in the case of linearly along x axis (a, b) and radially (c) polarized incident light focused using a high NA=0.9 lens in air. The plots are normalized to tlie peak (on axis) intensity liJol^ = |Bror(0,0)|^.

radially p o l a r i z e d l i g h t can result i n a very substandal r e s o l u t i o n i m p r o v e m e n t .

1.2.2. P R I N T I N G F O C U S E D S P O I S I N A P H O T O R E S I S T :

D I L L ' S M O D E L , I M-I O

-T O R S E S I S -T R E S P O N S E

W h e n f o c u s i n g i n a photoresist, i t is i m p o r t a n t to m o d e l the effect o f the l i g h t o n the m e d i u m . The photoresist exposure effect, when i t becomes less a b s o r b i n g a n d m o r e transparent, e v o l v i n g d u r i n g the i l l u m i n a t i o n , was m o d e l l e d by F. H . D i l l [I l j . The i n -tensity o f l i g h t Uz), passing t h r o u g h a h o m o g e n e o u s m e d i u m i n the z d i r e c t i o n , can be expressed v i a the Lambert's law:

Hz) = kexpi-az)

(1.3) Io exp ( - [apAcc + ap(co - c) -F ^ a/?Cfi)zJ,

w h e r e aPAC a n d CQ a n d are the m o l a r a b s o r p t i o n c o e f f i c i e n t a n d c o n c e n t r a t i o n o f the p h o t o a c t i v e c o m p o u n d before p h o t o c h e m i c a l reaction due to exposure, a p is the m o l a r a b s o r p t i o n c o e f f i c i e n t o f the p h o t o a c t i v e c o m p o u n d after exposure, c is the r e m a i n i n g a m o u n t o f the unexposed p h o t o a c t i v e c o m p o u n d after exposure, a n d the an a n d are the m o l a r a b s o r p t i o n coefficients a n d concentrations f o r each other c o n s t i t u e n t o f the photoresist. D i l l t h e n expressed the net c o e f f i c i e n t a according to:

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1.2. T m : r o c n s s i N d O F I . K M I T : VKOM T H F SCALAR T O T H E V E C T O R I A L A P I ' R O A C H 9

where

A^{apAc-ap)co, B = Y.aRCR + apCo,

These are k n o w n as the " D i l l parameters": A is the a d d i t i o n a l optical a b s o r p t i o n co-e f f i c i co-e n t bco-eforco-e co-exposurco-e, w h i l co-e B rco-eprco-esco-ents thco-e s u m o f all optical a b s o r p t i o n duco-e to c o m p o n e n t s o f the resist w h i c h are i n d e p e n d e n t o f the l i g h t exposure. M -1 a n d M = 0 correspond to unexposed and c o m p l e t e l y bleached photoresist, respectively. The q u a n -t u m e f f i c i e n c y is i n c o r p o r a -t e d i n "Dill's parame-ter" C:

f

= - C / M , (1.6)

where I a n d t represent i n t e n s i t y o f light a n d time, correspondingly.

Figure 1.8: Influence of the photoresist dissolution rate function on the crosssecdonal geometry after etching due to the pattern in tlie exposed photoresist.

The response o f a photoresist can be d e f i n e d as its d i s s o l u t i o n rate, w h i c h is a f u n c -t i o n o f an exposure dose. This charac-teris-tic o f a pho-toresis-t de-termines a crossec-tion g e o m e t r y o f the p a t t e r n i n a photoresist u p o n exposure. C o n v o l u t i o n o f the l i g h t i n -tensity p a t t e r n a n d the photoresist response f u n c t i o n determines the shape o f the p r i n t f r o m the exposed photoresist (Fig. I ii). I n tiie case o f a photoresist w i t h a n o n l i n e a r re-sponse, there is a threshold exposure, after w h i c h the photoresist's s o l u b i l i t y increases. No change i n the s o l u b i l i t y o f the photoresist takes place u n t i l tiiis threshold is reached.

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10 1. i N T H O n U C T I O N

It is t h e n possible to make a crossection w i t h steep edges using such a photoresist. I f the d i s s o l u t i o n response o f the photoresist is l i n e a r t h e n the r e s u l t i n g p a t t e r n due to a sinusoidal exposure w i l l itself have a sinusoidal crossection.

I n Subsec. 1.2.1 we show that one m u s t take i n t o account n o t o n l y a m p l i t u d e b u t the p o l a r i z a t i o n a n d phase o f the electric f i e l d , w h e n c o n s i d e r i n g the effect o f the i l l u m i n a -t i o n f r o m a h i g h - N A lens focussed inside -the pho-toresis-t. This is d o n e i n A p p e n d i x I )

a n d Appendix H o f the Chapters I ( ] o n i i n e r c i a l Resist a n d Ci Polarization-selective Resist. T h e d e r i v a t i o n employs the vector Richards-Wolf integral, a n d i t is presented i n d e t a i l i n [10, 11, 14-18].

1 . 3 . P R O I E C T " H I G H R E S O L U T I O N L I T H O G R A P H Y U S I N G U N

-C O N V E N T I O N A L P O L A R I Z A T I O N S T A T E S O F L I G H T "

The p r i m a r y m o t i v a t i o n o f the project "High r e s o l u t i o n o p t i c a l h t h o g r a p h y u s i n g u n c o n -v e n t i o n a l p o l a r i z a t i o n states o f l i g h t " is the e x p e r i m e n t a l realization o f laser beams w i t h specially shaped a m p l i t u d e , phase a n d p o l a r i z a t i o n d i s t r i b u t i o n at the i n p u t p u p i l o f a h i g h n u m e r i c a l aperture lens w i t h the a i m o f r e d u c i n g the effective spot size o f the f o -cused f i e l d b e l o w that o f the c o n v e n t i o n a l d i f f r a c t i o n l i m i t . This m o t i v a t i o n originates f r o m recent theoretical works [ I '.">, 10, 20]. They show that w h e n the p o l a r i z a t i o n state o f the l i g h t b e a m is radial a n d w i t h a p a r t i c u l a r radial a m p l i t u d e d i s t r i b u t i o n at the p u p i l o f the lens, a very tight spot can be achieved by means o f the l o n g i t u d i n a l ( i n the d i r e c t i o n of propagation) electric c o m p o n e n t o f the focused field.

This r e d u c t i o n o f the effective PSF can be used i n various applications such as laser w r i t i n g , mastering, o p t i c a l data storage, c o n f o c a l microscopy, a n d o p t i c a l tweezers. A n -other possible u t i l i z a t i o n o f l o n g i t u d i n a l p o l a r i z a t i o n i n the f o c u s e d field is i n fluores-cence microscopy. By t a i l o r i n g the field at the p u p i l , the p o l a r i z a t i o n o f the field at f o c u s can be o p t i m i z e d so tiiat the selective fluorescence can be excited since this occurs f o r molecules whose d i p o l e m o m e n t s are i n the d i r e c t i o n o f the electric field.

One p r o b l e m that l i m i t s the a p p l i c a t i o n o f this p r i n c i p l e is that the l o n g i t u d i n a l c o m -p o n e n t is n o t the o n l y one -present i n the f o c a l region (see Fig. i i >). Thus one has to i m p l e m e n t techniques w h i c h are sensitive o n l y to the l o n g i t u d i n a l electric field c o m p o nent. I n this regard, this p r o j e c t is done i n c o l l a b o r a t i o n w i t h the U n i v e r s i t y o f E i n d h o v e n where a p o l a r i z a t i o n sensitive resist has been developed so that exposure is l i m i t e d m a i n l y to one p o l a r i z a t i o n c o m p o n e n t . The p r o j e c t " H i g h r e s o l u t i o n o p t i c a l l i t i i o g -r a p h y using u n c o n v e n t i o n a l p o l a -r i z a t i o n states o f l i g h t " is the STW (Stichting Technische Wetenschappen) p r o j e c t #10727 c o n d u c t e d i n the f r a m e w o r k o f a c o l l a b o r a t i o n b e t w e e n the Optics Research G r o u p o f T U D e l f t a n d the Polymers i n Advanced Systems G r o u p o f T U / e i n v o l v i n g t w o PhD students ( i n o p t i c a l physics a n d i n chemistry). The goal o f the o p t i c a l c o m p o n e n t o f the project, w h i c h is the subject o f this thesis, is to o p t i m i z e the field at the p u p i l i n order to o b t a i n a narrow, large l o n g i t u d i n a l electric field c o m p o -n e -n t i-nside the photo-resist. The c h e m i s t r y aspect of the project aims to i-nvestigate a -n d synthesize a photo-resist w h i c h is sensitive o n l y to the l o n g i t u d i n a l c o m p o n e n t o f radiation. This t o p i c is t h o r o u g h l y described i n Ref.[?l ] . For applications i n direct laser w r i t

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-1.4. T i l l ; SI l u i c m i i i Ol- n i i : Tiii:sis 11

i n g technology a n d p o i n t per p o i n t optical lithography, the spot size inside the p h o t o r e -sist a n d the properties of the photore-sist are of crucial i m p o r t a n c e . This thesis presents proofs of the p r i n c i p l e w h i c h opdmizes these parameters i n c o m p a r i s o n to t r a d i t i o n a l lithography. B o t h p r o o f s of p r i n c i p l e demonstrate a factor o f t w o decrease i n spot size c o m p a r e d to the c o n v e n t i o n a l A i r y p a t t e r n inside the photoresist. Focused a m p l i t u d e m o d u l a t e d radially polarized l i g h t inside the c o m m e r c i a l isotropic photoresist is used i n i m p l e m e n t a t i o n of the first p r o o f o f the p r i n c i p l e . The second p r o o f o f the p r i n c i p l e is realized by means o f focussing radially p o l a r i z e d l i g h t inside a polarization-selective photoresist.

1 . 4 . T f ^ E S T R U C T U R E O F T I I E T H E S I S

Chapter 2 Fxperiinental Set-up, Methotls and I n s t r u m e n t a t i o n is dedicated m o s ü y to the

e x p e r i m e n t a l set-up f o r generating a m p f i t u d e m o d u l a t e d radially polarized l i g h t w i t h a specific a m p l i t u d e p r o f i l e to be focused o n a sample coated w i t h a t h i n layer o f p h o -toresist. The p r o d u c t i o n o f radially polarized l i g h t w i t h u n i f o r m phase f o r m e d u s i n g a circular w i r e g r i d polarizer (WGP) a n d spiral phase plate (SPP) is described. The a m -p l i t u d e m o d i ü a t i o n of n e a r - U V l i g h t has been o b t a i n e d u s i n g a s-patial light m o d u l a t o r (SLM). Discussion of SLM t u n i n g a n d testing f o r the wavelength of interest is i n c l u d e d . Finally, the procedures f o r the p r e p a r a t i o n of c o m m e r c i a l a n d p o l a r i z a t i o n selective re-sist samples are presented.

One o f the key c o m p o n e n t s f o r p r o d u c i n g radially polarized l i g h t at near-UV w a v e l e n g t h range a n d p a r t i c u l a r l y f o r A = 405 n m is tire WGP. Chapter:! Wire Cii id Polarizer covers a design of the WGR f o l l o w e d by f a b r i c a t i o n a n d experimental testing of the device. Theo-retical research, based o n Finite Element m e t h o d (FEM) w h i c h rigorously solves f o r the electromagnetic field numerically, indicates geometries a n d materials f o r the realization o f the WGP. The theoretical p r o o f of a procedure w h i c h obtains a circularly s y m m e t r i c radial p o l a r i z a t i o n w i t h constant phase is presented. The f a b r i c a t i o n procedure based o n the final recipe w i t h a detailed explanation of every f a b r i c a t i o n step is p r o v i d e d . Per-f o r m a n c e results Per-f r o m tests u s i n g the WGP to shape h i g h q u a l i t y radially polarized l i g h t for tight f o c u s i n g applications are shown. P r i n t i n g of spots smaller t h a n c o n v e n t i o n a l A i r y spots by f o c u s i n g a m p l i t u d e m o d u l a t e d radially polarized light o n c o m m e r c i a l p h o -toresists is t h o r o u g h l y described i n the Chapter 1 Comniereittl Resist. M o d e l l i n g of the l o n g i t u d i n a l a n d the transverse electric field c o m p o n e n t s p e r f o r m e d using a rigorous s o l u t i o n o f the Richards-Wolf d i f f r a c t i o n integral. Experiments i n w h i c h the a m p f i t u d e i n the p u p i l plane is tailored are realized using a SLM such as r e d u c i n g the apertures a n d o p t i m i z a t i o n of the field. We provide results f r o m inspecting the resulting stiuctures us-ing A F M to i n f e r the spot sizes.

Chapter Ti I'olarization selective Resist discusses p r i n t i n g o f focused spots i n

polariza-t i o n selecpolariza-tive a n d p o l a r i z a polariza-t i o n isopolariza-tropic resispolariza-t. The m e polariza-t h o d o f o b polariza-t a i n i n g spopolariza-ts smaller t h a n the c o n v e n t i o n a l Airy disc c o m b i n i n g the properties of p o l a r i z a t i o n selective resist a n d focussing n e a r - U V radially polarized l i g h t is described. A brief overview of polarizationselective resist synthesizing, its p r e p a r a t i o n and a p p l i c a t i o n o n tire substrate is f o l -l o w e d by detai-ls o n the exposure a n d post exposure procedures a n d A F M i n s p e c t i o n of the restilting structures. Polarization selectivity of the p o l a r i z a t i o n selective photoresists a n d p r o o f o f the p r i n c i p l e f o r o b t a i n i n g smaUer spots c o m p a r e d to the usual A i r y disc by

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12 R H i - E i i i: N{ ; i; s

h i g h q u a l i t y radially polarized light are described.

I n Chapter li (Joiicliisious, the conclusions are presented.

Finally, i n the appendices, we present the d e r i v a t i o n of equations f o r h i g h n u m e r i c a l aperture f o c u s i n g linearly a n d radially p o l a r i z e d l i g h t i n the f r a m e w o r k of vector Richards-W o l f d i f f r a c t i o n theory, l i s d n g of a LabView p r o g r a m used i n the e x p e r i m e n t a l procedure of exposing the photoresist, details o f the WCP f a b r i c a t i o n a n d i n s p e c t i o n a n d analysis of focused spots using c o m m e r c i a l resist.

R E F E R E N C E S

[1] A. Pizzagalli, C. Troadec, a n d f. Azemar, Photolithography equipment and materials for advanced packaging, MEMS and LED applications. Tech. Rep. (Yole D é v e l o p p e -m e n t , 2015). [2] Retrieved f r o m h t t p ://V;WVJ . i n f o w o r l d . c o m / a r t i c l e / 2 9 4 9 1 5 3 / h a r d u a r e / i n t e l - p u s h e s - l O n m - c h i p m a k i n g - p r o c e s s - t o - 2 0 1 7 - s l o w i n g - m o o r e s - l a w . h t m l (accessed November 10, 2015). [3] Image d o w n l o a d e d f r o m h t t p s : / / e n . v j i k i p e d i a . o r g / w i k i / S e m i c o n d u c t o r _ d e v i c e f a b r i c a t i o n (accessed N o v e m b e r 10, 2015).

[4] H . Gatzen, V Saile, a n d f. L e u t h o l d , Micro and Nano Fabrication. Tools and

Pro-rr.s.M-.s (Springer, Berlin, 2015).

[5] Image d o w n l o a d e d f r o m www. n a n o s c r i b e . de (accessed December 15, 2015).

[6] M . B o r n a n d E. Wolf, Principle-'^ of opiics Screiiih Edilinii (Cambridge U n i v e r s i t y

Press, 1999) pp. 1-952.

[7] 1. W. G o o d m a n , Introduction to Fourier Optics Second Edition (The M c G r a w - H i l l companies, inc., 1996) pp. 1-441.

[8] E. Hecht, Optics Fourth Edition (Addison Wesley, 2002) pp. 1-698.

[9] V.S. Ignatowsky, P a p e r s f y a « r f V ; rraiis. O p l . Insl. Pelrograd 1(4), 1 (1919).

[10] E. Wolf, Electromagnetic diffraction in optical systems. I. An integral representation of tite image field, I'roceetlings of the Royal Society of L o i i t l o n /\: Mathemaiic nl, Physical and Engineering Sciences 253,349 (1959).

[11] B. Richards a n d E. Wolf, Electromagnetic diffraction in optical systems. II. Structure ofthe image field in an aplanatic system, Proceedings o f t h e Royal Society of L o n d o n /\: M a l l i e n i a l i c a l , Physical and Rngitiecritig Sciences 253, 358 (1 9,59).

[12] A. v a n de Nes, L. Billy, S. Pereira, a n d ] . Braat, Calculation ofthe vectorial field distri-bution in a stratified focal region of a liigh numerical aperture imaging system, 0 | ) i , i:x|)ress 12, 1281 (2004).

[131 H . Levinson, I'riiu-iplcs of l.iihogiriphy. Ihirrl tzditioii rs/'//: Press Monograph. \

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R E i - i ; R i; N c r , s 13

[14] H . R U r b a c h a n d S. E Pereira, Focused fields of given power with maximum electric field components, Piiys. Rev. A 79, 01382,5 (2009).

[151 H . R U r b a c h and S. E Pereira, Field in focus with a maximum longitudinal electric component, I'hys. Rev, Lett, 100, 123904 (2008).

[16] S. Stallinga, Axial birefi ingence in high-numerical-aperture optical systems and the light distribution close to focus, i O p l . Sdc. A m . A 18, 2846 (2001).

[17] G. Z h o u , A. Jesacher, M . Booth, T. Wilson, A. R ó d e n a s , D. jaque, and M . Gu, Ax-ial birefi ingence induced focus splitting in lithium niobate. Opt Exjiress 17, 17970 (2009).

[18] S. Wang, X. Xie, M. Gu, a n d 1. Z h o u , Optical sharper focusing in an anisotropic crys-tal, j . Opt, Soc. A m . A 32, 1026 (2015).

[19] S. Quabis, R. D o r n , M . Eberler, O. Glöckl, and G. Leuchs, Focusing light to a tighter spof, Opiics C o n n n u i i i e a t i o n s 179, 1 (2()()()).

[20] R. D o r n , S. Quabis, and G. Leuchs, Sharper focus for a radially polarized light beam, Phys, Rev. Lett, 9 1 , 233901 (2003).

[21] M.-R Van, C. C. L. Schuurmans, C. W. M . Basdaansen, a n d D. I . Broer, Polarization-selective polymerization in a photo-crosslinking monomer film, RSC Adv. 4, (i2-l9!) (2014).

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A P P E N D I X A

F o l l o w i n g the lines of [ i , 1, we give the expressions of the electromagnetic f i e l d i n focus for the cases of linear and radial p o l a r i z a t i o n , c o n t i n u i n g discussion f r o m Eq. 1.2 o f Chapter ! I n i i o c l u c l i o n.

A t i m e - h a r m o n i c electromagnetic field w i t h w > 0 propagates i n positive z-cfirection i n respect to the Cartesian coordinate system (x, y, z). W h e n focused i n a homogeneous n o n a b s o r b i n g m e d i u m o f a refractive index n, i t can be described as an angular spec-t r u m of plane waves: E(r) = - ^ f f , A{kr,ky)exn{ik-r]dk^dky. 4^ (1.7) 1 1 H(r) = — r 1/ , k x A(A:v,/cv)exph'k'r dfcvdfcy. An^ ojpo JJJkl+klskoNA • i t-K J • y

kx, ky, kz are c o m p o n e n t s of k w i t h kz = {k^n^ - k^ - ky)^'^, where ko = ZTT/AQ. N A : nsin(ö,„„.v).

U n i t vectors x, y, z of the Cartesian coordinate system are expressed as:

x=sin(0)cos(0)k-i-cos(0)cos(0)0-sin((/))</>,

y = sin(0) sin((/))k -i- c o s ( ö ) sm((p)è + cos(0)0, (1.8) z = c o s ( 0 ) k - s i n ( 0 ) ê .

Positively o r i e n t e d o r t h o n o r m a l basis k , 0 , 0 of the spherical coordinate system i n the reciprocal k space is d e f i n e d as:

k = sin(0) cos(0)x-l- s i n ( ö ) sin(0)y + cos(0)z,

0 = cos(0) cos(0)x-f cos(0) sin((/))y- sin(0)z, (1.9) ^ = - s i n ( 0 ) x + cos(0)y,

where 0 < 0 < 9,„„x, 0<(p<27T are polar a n d a z i m u t h a l angles, correspondingly.

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16 A I ' P I ; N I ) I X A

k=ko nk a n d the Jacobian of the t r a n s f o r m a t i o n of spherical coordinates 9, (p i n t o k c o m

-ponents fcv, ky is w r i t t e n :

W fcos(0)cos((/)) -sin(0)sin((/))^

Sky^ - ' ^ o " cos(0)sin{0) sin(0)cos(0) j ^^ ' \ 66 S(l> I

a n d dkxdky = fc^n^ cos(0) s i n { 0 ) d 0 d 0 .

Since the electric f i e l d is free of divergence (A-k = 0), the vector a m p l i t u d e A can be given by:

A{B,(p) = Ag[e,(p)d + A^{e,cp)^. (1.11)

A p p l y i n g the p r o p e r t y o f o r t h o n o r m a l i t y o f u n i t vectors:

k x 0 = <^, 0x(/. = k, 0 x k = 0, (1.12)

we get

kxA^kon(-A^9 + Ae^). (1.13)

Finally, electromagnetic f i e l d i n focus can be r e w r i t t e n as:

7,2 pdinax r^n E(r) = — / (A00-t-A0(^)cos(0)sin(0)exp(/k-r)d0d(/) J o JO H(r) = ^ — ƒ ( - A 0 0 - t - A e 0 ) c o s ( 0 ) s i n ( 0 ) e x p ( z k - r ) d 0 d 0 AiKlJol J o Jo (1.14)

Let consider a t r a n s f o r m a t i o n of a p u p i l f i e l d f r o m polar coordinate system (pp,q)p) i n t o the Cartesian coordinate system [Xp, yp,Zp):

^p{Pp,(Pp) = EpiPp<(Pp)Pp + Ell,{pp,(Pp)(Pp, (1.15)

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A l ' l' l N D I X A 17

(1.16)

(pp = - sm[(pp)x+ cos{(pp)y

A c c o r d i n g to [ - ] , a m p l i t u d e of the plane waves i n the focal plane can be w r i t t e n as:

A(k„ky) = -2ni ƒ M ( k ) E 4 - ( ^ , - ( ^ ) , (1.17) [kon]^'^kl'^ [ kon kon)

where ƒ is the focal distance o f the lens and a m a t r i x IVI(k) rotates the p u p i l electric f i e l d u i t h e direction p e r p e n d i c u l a r to the wave vector k = konism{9) cos((/))k+sin(0) sm{(p)d+ cosi6)(p) so that

M(.ml'ipp,<pp) = -Ep-E!^^. (1.18)

Pupil polar coordinates Pp and (pp can be expressed t h r o u g h spherical coordinates 0 and

P p = / s i n ( 0 ) , <pp=(p + n, (1.19)

so t h a t

A ( 0 , 0 ) = -2ni ^ M{0, (p)E>'(- ƒ sin(0) cos(0), - ƒ sin(0) sin(0)) =

konVcosW)

f \ D, (1.20)

- 2 ; r i ; E'i - ƒ sin(0) cos((/)), - ƒ sin(0) s i n ( é ) 0+ fcoAivcos(0) ^

- ƒ sin(0) cos(0), - ƒ sin(0) sin(0))(/>

Linearly x-polarized plane wave can be expressed w i t h respect to the polar basis i n the p u p i l of a lens:

Ep[pp,(Pp) = cos[(pp) El^{pp,ipp)^-sm(,q>p) (1.21)

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18 A I ' I ' I ; N L ) 1 X A

ƒ cos(rf)) ƒ sinié)

Ae{e,(t>)=2ni-f A^(B.cp) = - 2 n i - ^ — ^ , (1.22) kon \/cos(0) A:o« \/cos(0)

Hence,

f

A{B,(p) = 2jii ; cos(0)0-sin(0)(/»

A;on\/cos(0) J = 27r/- ƒ : (cos(0)cos2((^) + sin2(0))x A:on\/cos(0) + (cos(0) - l ) c o s ( 0 ) s i n ( 0 ) y - s i n ( 0 ) c o s ( ( / ) ) z , - A ^ ( 0 , 0 ) 0 + Ae ( 0 , 0 ) 0 = (1.23) f \ -]

2ni ;^ sin(0)0 + cos(0)0

A:on\/cos(0) J

= 2;r(- ƒ : (cos(0) - l ] c o s ( 0 ) s i n ( 0 ) x

fco/ï\/cos(0)

+ (cos(0) sin^ (0) + cos^ (0))y - sin(0) cos(0)z

I n order to achieve m a x i m u m o n axis l o n g i t u d i n a l c o m p o n e n t i n focus [' ], radially polarized light w i t h a m o n o t o n i c a l l y increasing a m p l i t u d e f r o m the centre to the p e r i p h -ery o f the p u p i l can be i m p l e m e n t e d . Such a m p l i t u d e d i s t r i b u t i o n can be expressed w i t h respect to tlie polar basis i n the p u p i l of a lens as:

(1.24)

I n the case of radially polarized p u p i l f i e l d

Ae{e,(P) = 2jii-^ ^ 7 = F ' >l0(Ö,0) = O, (1.25) kon Av^cos(0)

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Ui l I lil :\<:rs 19

^ . j ; , ^ ^ J M 2 ^^^^^^^^^^^ 1 ^ ^ ^ (1.26)

Po Ao Po 3 3

is the Lagrange m u l t i p l i e r , o b t a i n e d under the constraint o f the constant m e a n power f l o w Po (see Appendix I) f o r details).

Hence,

AA;o«\/cos(ö)

-2jr/ — / t a n ( 0 ) _ (.^g^g^ cos(0)x-l- cos(9) sin(rf))y - s i n ( ö ) z AA:onVcos(0) -A^{e,<p)0 + Ag{9,(P)^^-2ni—^~^l=4> Akonvcosid) / t a n ( 0 ) r = -2ni -^=^ -sm((/))x-l-cos(0)y (1.27) AAro/ïVcösïëy P v E F H R E N C E S

[1] H . R U r b a c h a n d S. P. Pereira, Field in focus with a maximum longitudinal electric component, I'liys. Rev. Lett. 100, 123904 (200H).

[2] H . R U r b a c h a n d S. F. Pereira, Focused fields of given power with maximum electric field components, Phys. Rev. A 79, 01382,5 (2009).

[3] V. S. Ignatowsky, PapersP/and V, l i ans. Opt. Itist, Peltograd 1(4), 1 (1919).

[4] E. Wolf, Electromagnetic diffraction in optical systems. I. An integral representation of the image field, Proceedings o f t h e Royal Society of London A: M a l h e i n a l i c a l , Physi-cal and iTit;ineering Sciences 253,349 (1959).

[5] B. Richards and E. Wolf, Electromagnetic diffraction in optical systems. IL Structure of the image field in an aplanatic system, Pioceedings of the Royal Soriet\' ol' London A: Mtitheniatical, Physical and Enginecting Sciences 253, 358 (1959).

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2

E X P E R I M E N T A L S E T - U P , M E T H O D S

A N D I N S T R U M E N T A T I O N

This chapter is dedicated to the experimental set-up to generate ü g h t f o c a l spots w i t h a large l o n g i t u d i n a l c o m p o n e n t inside the photoresist. The w o r k i n g p r i n c i p l e o f the c r u -cial elements a n d details o f the experimental procedures are p r o v i d e d . A spe-cial atten-t i o n is given atten-to a d e s c r i p atten-t i o n o f c o m b i n a atten-t i o n o f spaatten-tial l i g h atten-t m o d i ü a atten-t o r wire g r i d izer a n d spiral phase plate to shape the o p t i m u m a m p l i t u d e m o d u l a t e d radially polar-ized l i g h t b e a m w i t h all p o i n t s i n phase. The optical c o m p o n e n t s a n d the e x p e r i m e n t a l a l i g n m e n t procedure, photo-resist preparation, exposure and sample scanning methods all characterized.

2 . 1 . G E N E R A L D E S C R I P T I O N

I

N this section we show the e x p e r i m e n t a l set-up designed a n d b u i l t to achieve the goal of the project, i.e. to get a large l o n g i t u d i n a l l y p o l a r i z e d c o m p o n e n t inside the p h o -toresist a n d hereby to realize a smaller focused spot t h a n a c o n v e n t i o n a l Airy spot f o r the same wavelength a n d n u m e r i c a l aperture.[ I ] .

A n overview o f the set-up key c o m p o n e n t s a n d their positions; a source; o p t i c a l ele-ments to achieve a m p l i t u d e , p o l a r i z a d o n and phase shaping; a f o c u s i n g lens; a sample holder a n d sample scan d r i v i n g electronics is presented w i t h details.

A scheme o f the setup is s h o w n i n Fig ' 1 . The light b e a m e m i t t e d by a 405 n m a diode laser is shaped to a p p r o x i m a t e l y a t o p - h a t f u n c t i o n by a c o l l l m a t i o n lens. The b e a m passes a polarizer (GLPl) a n d a beamsplitter (BSl) that directs i t to a reflective spadal light m o d u l a t o r (SLM) to achieve a m p l i t u d e m o d u l a d o n ( m o d u l a t e d after GLP2). W i t h the c o m b i n a d o n o f a quarter waveplate (A/4), a wire g r i d polarizer (WGP) a n d a spiral phase plate (SPP), the b e a i n is converted f r o m linear to radial p o l a r i z a d o n w i t h a f l a t

phase (as explained i n Chapter 3 Wire (, rid I'olari/ci i n details). Finally, a 0.9 NA lens ( L l )

focuses the laser beam o n t o a glass sample c o n t a i n i n g a t h i n layer o f photoresist. The sample is m o u n t e d o n a 3D piezo cube w i t h a scan range o f 100 p m f o r all axes. The laser

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22 2. E x i ' i ; i i i M i ; N T A L SI;T-I)I>, M i n n o n s A N D I N S T H U M I - N T A T I O N

GLP3

with tlie iiicoupler Camera connected to tlie outcoupler

I via single mode fiber

Figure 2.1: The schematics ofthe complete setup:Blue diode laser (405 nm); Colllmation lens; DM1: dichroic mirror; M2-M3: mirrors for A = 405 nm; FM4: flipping mirror to switch between linearly and radially polarized arms ofthe set-up; GLP1-GLP3: Glan-Laser polarizers; BSl, BS2: beam splitters; A/4 quarter wave plate; WGP-wire grid polariser; SPP - spiral phase plate for A = 407 nm; CCD camera; L l : high NA Objective lens with NA = 0.9; L2: low aperture focusing lens. The sample with photo-resist is mounted on a 3D scan piezo table (100 microns per axis). The HeNe laser (633 nm) is used for alignment purposes,

exposure t i m e and tiie p o s i t i o n of the scan table are c o n t r o l l e d w i t h a LabView software. The polarization-selective resist sample is m o u n t e d i n a closed box (Black container) w h i c h is p u m p e d w i t h n i t r o g e n d u r i n g the exposure, because the p o l a r i z a t i o n sensitive resist reacts o n l y i n a n oxygen-free e n v i r o n m e n t .

2 . 2 . L , ' \ S I;K S O U R C E

The l i q u i d crystal p o l a r i z a t i o n selective photoresist is sensitive i n the near U V wave-length range of AA = 193-405 n m . Blue diode N i c h i a laser (Blue diode laser) of 405 n m w i t h a laser driver f a b r i c a t e d at Philips Research is used as a source. The measured laser s p e c t r u m is presented i n Fig a.

A specially designed f o r the wavelength A = 405 n m c o l l i m a t i o n lens is i n c o r p o r a t e d i n the same holder as the laser head w i t h possibility of the p o s i t i o n a d j u s t m e n t to achieve the best coUimation. The laser power as a f u n c t i o n o f laser diode c u r r e n t is s h o w n i n the graph of Fig b.

The 633 n m HeNe red laser is used f o r a l i g n m e n t procedures w i t h subsequent v e r i -fication of o v e r l a p p i n g of the t w o beams (red a n d blue) at several c o n t r o l locations along the b e a m p a t h . It has an i m p o r t a n t role i n the f o c u s i n g procedure i n the case o f c o m -mercial resist (see Sec. '.;>).

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